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Year 8 Factorising Expressions (Common Factors) Worksheet — Level 2 — Practice Set 4 — Answers

Answer sheet with worked solutions for the Year 8 algebraic expressions worksheet.

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Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Algebraic Expressions

Year 8 Factorising Expressions (Common Factors) Worksheet — Level 2 — Practice Set 4 — Answers

Find the highest common factor of the terms and write it outside the brackets.

1.Factorise fully: 8m − 36n

Answer: 4(2m − 9n)

  1. Highest common factor: 4
  2. 8m − 36n = 4(2m − 9n)
  3. Check by expanding the brackets.
2.Factorise fully: 6x2 + 2x

Answer: 2x(3x + 1)

  1. Highest common factor: 2x
  2. 6x2 + 2x = 2x(3x + 1)
  3. Check by expanding the brackets.
3.Factorise fully: 40x − 64y

Answer: 8(5x − 8y)

  1. Highest common factor: 8
  2. 40x − 64y = 8(5x − 8y)
  3. Check by expanding the brackets.
4.Factorise fully: 3x2 + 2x

Answer: x(3x + 2)

  1. Highest common factor: x
  2. 3x2 + 2x = x(3x + 2)
  3. Check by expanding the brackets.
5.Factorise fully: 12x − 8y

Answer: 4(3x − 2y)

  1. Highest common factor: 4
  2. 12x − 8y = 4(3x − 2y)
  3. Check by expanding the brackets.
6.Factorise fully: 18x2 + 42x

Answer: 6x(3x + 7)

  1. Highest common factor: 6x
  2. 18x2 + 42x = 6x(3x + 7)
  3. Check by expanding the brackets.
7.Factorise fully: 16m + 72n

Answer: 8(2m + 9n)

  1. Highest common factor: 8
  2. 16m + 72n = 8(2m + 9n)
  3. Check by expanding the brackets.
8.Factorise fully: 9x2 − 3x

Answer: 3x(3x − 1)

  1. Highest common factor: 3x
  2. 9x2 − 3x = 3x(3x − 1)
  3. Check by expanding the brackets.
9.Factorise fully: 36m + 9n

Answer: 9(4m + n)

  1. Highest common factor: 9
  2. 36m + 9n = 9(4m + n)
  3. Check by expanding the brackets.
10.Factorise fully: 4x2 − 14x

Answer: 2x(2x − 7)

  1. Highest common factor: 2x
  2. 4x2 − 14x = 2x(2x − 7)
  3. Check by expanding the brackets.
11.Factorise fully: 36m − 27n

Answer: 9(4m − 3n)

  1. Highest common factor: 9
  2. 36m − 27n = 9(4m − 3n)
  3. Check by expanding the brackets.
12.Factorise fully: 8x2 + 6x

Answer: 2x(4x + 3)

  1. Highest common factor: 2x
  2. 8x2 + 6x = 2x(4x + 3)
  3. Check by expanding the brackets.
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